This phase II trial studies how well radiation therapy and docetaxel work in treating patients with human papillomavirus (HPV)-related oropharyngeal cancer. Radiation therapy uses high-energy x-rays to kill tumor cells. Drugs used in chemotherapy, such as docetaxel, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving radiation therapy with docetaxel my kill more tumor cells.